Question

What is the transformation of f(x)= x^3:

Answer 1

Answer:

7. Down 5

8. Horizontal Reflection.

9. Vertical Stretch by a factor of 5.

Explanation:

Parent function: f(x) = x^3

7. f(x)= x^3 - 5

Comparing it with f(x) - d which gives function shifted d units down.

Here the function has shifted 5 units down.

8. f(x)= -x^3

Comparing with -f(x) gives reflection over x-axis (horizontal reflection).

Here the function f(x) = (-1x^3) has been reflected horizontally.

9. f(x)= 5x^3​

Comparing with a(f(x)) gives vertical stretch when |a| > 1 or compression when 0 < |a| < 1 by a factor of a.

Here the function f(x) = 5x^3​ has been vertically stretched by a factor of 5.

Answer 2

Answer:

7.  Down 5

8.  Horizontal reflection

9.  Vertical stretch by a factor of 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a$

$y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}$

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

$y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}$

Identify the transformations that take the parent function to the given function.

Question 7

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=x^3-5$

Comparing the parent function with the given function, we can see that 5 has been subtracted from the parent function.

Therefore, the transformation is:

$f(x)-5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units down}$

Question 8

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=-x^3$

Comparing the parent function with the given function, we can see that the parent function has been multiplied by -1.

Therefore, the transformation is:

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

Question 9

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=5x^3$

Comparing the parent function with the given function, we can see that the parent function has been multiplied by 5.

Therefore, the transformation is:

$y=5\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:5$

Learn more about graph transformations here:

brainly.com/question/27845947